Discrete artificial boundary conditions for the linearized Korteweg–de Vries equation. Issue 5 (22nd March 2016)

• Record Type: Journal Article
• Authors: Besse, C.; Ehrhardt, M.; Lacroix‐Violet, I.
• Is Part Of: Numerical methods for partial differential equations. Volume 32:Issue 5(2016:Sep.)
• Page Start: 1455
• Page End: 1484
• Publication Date: 2016-03-22
• Subjects: artificial boundary conditions -- KdV equation -- numerical simulation; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22058
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : We consider the derivation of continuous and fully discrete artificial boundary conditions for the linearized Korteweg–de Vries equation. We show that we can obtain them for any constant velocities and any dispersion. The discrete artificial boundary conditions are provided for two different numerical schemes. In both continuous and discrete case, the boundary conditions are nonlocal with respect to time variable. We propose fast evaluations of discrete convolutions. We present various numerical tests which show the effectiveness of the artificial boundary conditions.© 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 32: 1455–1484, 2016